Anthropic Reasoning and Perspective-Based Arguments

1. The world as we see it, appeared from nothing via some unknown process.

2. “Nothing” doesn’t have any properties by definition, so it doesn’t have a counter of worlds which appeared from it

Absolute metaphysical "nothing" also has no powers and no properties, so it had no power or property of universe creation. (Popular accounts of cosmology talk about universes appearing from nothing , but that is a loose usage of language).

All arguments depend on assumptions ,and yours is no exception.

For one thing , you are assuming fairly strong realism about time. That's not a feature of all theories, or even all multiversal theories. Tegmarks mathematical multiverse struggles to explain time as a subjective phenomenon.

N is the average number of civilizations per galaxy.

I was going to agree with this, but I realize I need to retract my earlier agreement with this statement to account for the difference between galaxies and the observable universe. We don't, in fact, have evidence for the "fact that N is at least 1." We have evidence that the number of civilizations in the universe is at least one. But this is likely to be true even if the probability of a civilization arising on any given galaxy is very low.

SDO treat N as the expected number of civilizations in the Milky Way, i.e. in our galaxy (page 2):

The Drake equation was intended as a rough way to estimate of the number of detectable/contactable civilizations in the Milky Way

If they interpret N in this way, then N is at least 1. They didn't account for this fact in a systematic way, even if some parameter estimations already should include some such considerations. (From your quote I don't find it clear whether this is really the case. Also SIA is a fairly new theory and as such unlikely to play a significant role in the historical estimates they looked at).

But what is it from a gods-eye perspective?

It doesn't seem meaningful to ask this.

It just occurred to me that you still need some prior probability for your sentence which is smaller than 1. If you condition on "My observations so far a ike-ish" and this statement for you has unconditional probability 1, then conditioning on it has not effect. Conditioning on a probability 1 statement is like not conditioning at all. But what is this prior probability and how could it be smaller than 1 for you? It seems to be necessarily true for you. I guess we are forced to consider some non-indexical (gods-eye) version of that statement, e.g. like the one I suggested in my last comment. Also your characterization of (your version of) SIA was quite informal, so there is room for improvement. My personal goal would be to make SIA (or a similar principle) nothing more than a corollary of Bayesian updating, possibly together with a general theory of indexical beliefs.

If some observer only has some probability of having had the same set of observations, then they get a corresponding weight in the distribution.

Good idea. Maybe it is not just the probability that the hypothetical observer had the same observations, it's the probability that the hypothetical observer exists and had the same observations. Not just what observations observers made is often a guess but also how many of them exist. Also, I don't think "had the same observations" is quite right to characterize the "total evidence". Because there could be observers like a Swamp Man (or Boltzmann brain etc) which have the same state of mind as you, and thus arguably the same total evidence, but whose memories formed just by accident and not because they actually made the experiences/observations they think they remember. So I think "has the same state of mind" is better to not exclude those freak observers to begin with, because we might be such a freak observer.

This breaks all Bayesian updates as probabilities become impossible to calculate.

I think you are referring to what is known as the measure problem in cosmology: What is the probability that a cow is two-headed if there are infinitely many one-headed and two-headed cows in the universe? Surely it is still much more probable that a cow is one-headed. There are apparently several solutions proposed in cosmology. For a universe with is spatially infinite I would estimate the probability of a cow to be one-headed by the ratio of the expected number of one-headed cows to the expected number of cows -- in a growing imaginary sphere around us. The sphere is of finite size and we take the probability of a cow being one-headed as the limit of the ratio as the size of the sphere goes towards infinity. Then surely the sphere at any finite size contains much more one-headed cows than two-headed cows (the latter are estimated at a much larger number because two-headedness is not evolutionary advantageous for cows). There are other proposed solutions. I think one can be optimistic here that probabilities are not impossible to calculate.

Which is a great reason to exclude infinite universes a priori.

I think the measure problem is merely a practical problem for us. Which would be an instrumental reason not to consider infinite universes if we don't like to work on the measure problem (if only considering universes with finite size has higher utility for us). But we would need an epistemic reason, in contrast to an instrumental reason, to a priori exclude a possibility by assigning it probability 0. I think there are three types of epistemic reasons to do this:

1. if we think that the idea of an infinite universe is logically contradictory (that seems not to be the case)

2. if we think that an infinite universe is infinitely unlikely (That seems only the case for infinite universes with infinite information content. But infinite universes can plausibly have finite and even low finite information content.)

3. If something is not the case to which we have direct epistemic access. I currently do not have a headache. Since we are perfectly competent in judging the contents of our mind, and a headache is in the mind, my probability of "I have a headache" is 0. (Unlike headaches and other observational evidence, infinite universes are not mental objects, so that option is also not viable here.)

To highlight the difference between practical/instrumental reasons/rationality and epistemic reasons/rationality: Consider Pascal's Wager. Pascal argued that believing in God has higher expected utility than not believing or being agnostic. Whether that argument goes through is debatable, but in any case it doesn't show that God exists (that his existence is likely). If subjectivly assigning high probability to a hypothesis has high utility, that doesn't mean that this hypothesis actually has high probability. And the other way round.

Such a infinite universe with pseudo randomness might be nearly indistinguishable from one with infinite information content.

I don't know how this is relevant.

You seemed to specifically object to universes with finite information content on grounds that they are just (presumably periodic) "loops". But they need not be any more loopy than universes with infinite information content.

I wrote two posts on this: https://www.lesswrong.com/posts/PSichw8wqmbood6fj/this-territory-does-not-exist [LW · GW] and https://www.lesswrong.com/posts/zm3Wgqfyf6E4tTkcG/the-short-case-for-verificationism [LW · GW]. I don't think ontological claims are meaningful except insofar as they mean a set of predictions, and infinite ontological claims are meaningless under this framework.

But you seem to be fine with anything on which you could possibly update. E.g. there could be evidence for or against the plane topology of the universe. The plane topology means the universe is infinitely large. And as I said, SIA seems to make the significant prediction that evidence which implies a finite universe has probability 0.

I know this opens a huge can of worms, but I also wanted to comment on this one:

By talking about the unseen causes of visible events, it is often possible for me to compress the description of visible events. By talking about atoms, I can compress the description of the chemical reactions I've observed. Sure, but a simpler map implies nothing about the territory.

If hypotheses (e.g. about the existence of hands and chairs and rocks and electrons and forces and laws) which assume the existence of things external to our mind greatly reduce the information content of our mental evidence, then those hypotheses are more likely to be true than a pure phenomenological description of the evidence itself. Because lower information content means higher a priori probability. If you entertained the hypothesis that solipsism is true, this would not compress your evidence at all, which means the information content of that hypothesis would be very high, which means it is very improbable. The map/territory analogy is not overly helpful here I think. If you mean with map "hypotheses", then simpler hypotheses do in fact (probabilistically) "imply" something about the world, because simpler hypotheses are more likely to be true.

Another point: There many people who say that the main task of science is not to make useful technology, or to predict the future, but to explain our world. If you have some evidence E and a hypothesis H, and that hypothesis is supposed to explain your evidence, then that explanation is correct if and only if the following is true:

E because H.

But the truth of any statement of the form of "y because x" arguably implies the truth of x and y. So H must be true in order to correctly explain your evidence. If H is true, and H asserts the existence of things external to your mind (hands, chairs, laws etc.) then those things exist. Almost any hypothesis talks about objects external to your mind. In fact, we wouldn't even call beliefs about objects internal to our mind ("I have a headache", "I have the visual impression of a chair in front of me", "I have a memory of eating pizza yesterday") hypotheses at all, we would just call them "evidence". If no external things exist, then all "y because x" statements would be false.

I'm not sure about your argument involving the "level IV multiverse". I think it is equivalent to modal realism (everything which possibly exists, exists). I'm not sure whether the information content of that hypothesis is high or low. (It is infinite if we think of it as a long description of every possible world. If the information content is very high, then the hypothesis is likely to be false, which would justify our belief that it is false. If it is in fact false, we have a justified true belief in the falsity of modal realism. Since this is not a Gettier case, we then would know that modal realism is false.)